Higher order group cohomology and the Eichler-Shimura map

Abstract

Higher order group cohomology is defined and first properties are given. Using modular symbols, an Eichler-Shimura homomorphism is constructed mapping spaces of higher order cusp forms to higher order cohomology groups.

Higher-order Maass forms

“…In the sequel, we will need a basis for I q+1 \I q . Arguing as in Lemma 2.1 in [5] we can deduce that the elements…”

Untitled

“…In the sequel, we will need a basis for I q+1 \I q . Arguing as in Lemma 2.1 in [Deitmar 2009], we can deduce that the elements…”

Higher order invariants in the case of compact quotients

“…L-functions of second order forms have been studied in [7], Poincaré series attached to higher order forms have been investigated in [14], dimensions of spaces of second order forms have been determined in [8,9]. Higher order cohomology has been introduced and an Eichler-Shimura type theorem has been proven in [4]. In [5] a program has been started which aims at an understanding of the theory of higher order forms from an representationtheoretical point of view.…”